The origin of anomalous Hall effect (AHE) in magnetic materials is one of the most intriguing aspects in condensed matter physics and has been a controversial topic for a long time. Recent studies indicate that the intrinsic AHE is closely related to the Berry curvature of occupied electronic states. In a magnetic Weyl semimetal with broken time-reversal symmetry, there are significant contributions to Berry curvature around Weyl nodes, possibly leading to a large intrinsic AHE. Here, we report the quite large AHE in the half-metallic ferromagnet Co3Sn2S2 single crystal. By systematically mapping out the electronic structure of Co3Sn2S2 both theoretically and experimentally, we demonstrate that the intrinsic AHE from the Weyl fermions near the Fermi energy is dominating. The intrinsic anomalous Hall conductivity depends linearly on the magnetization and can be reproduced by theoretical simulation, in which the Weyl nodes monotonically move with the constrained magnetic moment on Co atom.

Using magnetic band theory and topological indices obtained from Magnetic Topological Quantum Chemistry (MTQC), we have performed the first high-throughput calculations of 549 magnetic topological materials and have discovered 130 magnetic enforced semimetals and topological insulators, thereby enhancing by a factor of 10 the number of known magnetic topological materials. We use as our starting-point the Bilbao Magnetic Material Database, containing 549 non-ferromagnetic compounds whose magnetic structure and symmetry group have been painstakingly deduced from neutron-scattering experiments. This knowledge is crucial for correct ab initio calculations of the materials' band structure, which we have performed for each of those compounds -including complete phase diagrams at different values of Hubbard potential in LDA+U. Using an in-house code to be made publicly available for finding the magnetic co-representations at high symmetry points, we then feed this data into the topological machinery of MTQC to determine the topological materials, as well as the obstructed atomic limits. We then pick several candidates for showcasing new topological physics and analyze the topological trends in the materials upon varying interactions.